We propose a new duality involving topological strings in the limit of large
string coupling constant.
The dual is described in terms of a classical statistical mechanical model of
crystal melting, where the temperature is inverse of the string coupling
constant. The crystal is a discretization of the toric base of the Calabi-Yau
with lattice length $g_s$. As a strong evidence for this duality we recover the
topological vertex in terms of the statistical mechanical probability
distribution for crystal melting.
We also propose a more general duality involving the dimer problem on
periodic lattices and topological A-model string on arbitrary local toric
threefolds. The $(p,q)$ 5-brane web, dual to Calabi-Yau, gets identified with
the transition regions of rigid dimer configurations.